Imhof Lorens A, Fudenberg Drew, Nowak Martin A
Statistische Abteilung, Universität Bonn, D-53113 Bonn, Germany.
J Theor Biol. 2007 Aug 7;247(3):574-80. doi: 10.1016/j.jtbi.2007.03.027. Epub 2007 Mar 24.
The repeated Prisoner's Dilemma is usually known as a story of tit-for-tat (TFT). This remarkable strategy has won both of Robert Axelrod's tournaments. TFT does whatever the opponent has done in the previous round. It will cooperate if the opponent has cooperated, and it will defect if the opponent has defected. But TFT has two weaknesses: (i) it cannot correct mistakes (erroneous moves) and (ii) a population of TFT players is undermined by random drift when mutant strategies appear which play always-cooperate (ALLC). Another equally simple strategy called 'win-stay, lose-shift' (WSLS) has neither of these two disadvantages. WSLS repeats the previous move if the resulting payoff has met its aspiration level and changes otherwise. Here, we use a novel approach of stochastic evolutionary game dynamics in finite populations to study mutation-selection dynamics in the presence of erroneous moves. We compare four strategies: always-defect (ALLD), ALLC, TFT and WSLS. There are two possible outcomes: if the benefit of cooperation is below a critical value then ALLD is selected; if the benefit of cooperation is above this critical value then WSLS is selected. TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS.
重复囚徒困境通常被认为是一个针锋相对（TFT）的故事。这一非凡策略在罗伯特·阿克塞尔罗德的两场锦标赛中均获胜。针锋相对策略会重复对手上一轮的行为。如果对手合作，它就合作；如果对手背叛，它就背叛。但针锋相对策略有两个弱点：（i）它无法纠正错误（错误举动）；（ii）当出现总是合作（ALLC）的突变策略时，一群采用针锋相对策略的参与者会因随机漂移而受到影响。另一种同样简单的策略，即“赢则继续，输则改变”（WSLS），则不存在这两个缺点。如果结果收益达到其期望水平，“赢则继续，输则改变”策略会重复上一步行动，否则就改变行动。在这里，我们使用一种有限种群中随机进化博弈动力学的新方法，来研究存在错误行动时的突变 - 选择动力学。我们比较四种策略：总是背叛（ALLD）、总是合作（ALLC）、针锋相对（TFT）和“赢则继续，输则改变”（WSLS）。有两种可能的结果：如果合作的收益低于一个临界值，那么总是背叛策略会被选中；如果合作的收益高于这个临界值，那么“赢则继续，输则改变”策略会被选中。在这个进化过程中，针锋相对策略从未被选中，但它会降低“赢则继续，输则改变”策略的选择阈值。
